Which graph represents the solution to the compound inequality?

–2x + 4 ≤ 8 and –2x + 4 > –6

The function g(x) = x³ - 2

The function h(x) = 2x³

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

parent function = x³

As, function is shifted vertically down by 2 units to obtain g(x).

So, g(x) = x³ - 2

function h(x) Horizontally by a factor of 2, to obtain, h(x).

So,  h(x) = 2x³

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Answer:

this is a cube so it has 6 faces

Hope This Helps!!!

Answer:

To find the vertical distace between both points you will have to add both. 8,586+10,911= 19 497.

Hence, the vertical distance is 19,497 feet.

Here is a picture:
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The value of c is 3

The complete question is in the attached image

The function definition is given as:

g(x) = f(x) - c

From the graph of functions f(x) and g(x), we can see that:

f(x) is shifted down by 3 units to get to g(x)

This means that:

g(x) = f(x) - 3

By comparing g(x) = f(x) - 3 and g(x) = f(x) - c,

We have:

c = 3

Hence, the value of c is 3

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Answer:

332519000 in scientific notation is 3.32519 x 10^8

Step-by-step explanation:

Hope that helped

Answer:

The form is a * 10ᵇ where 0 < a < 10

Answer:

4x + y = 1

Step-by-step explanation:

Start with the familiar format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

With a slope of -4, we can write:

y = -4x + b

We need to find a value for b that forces the line through point (1,-3).  This is done by entering this point in the equation and solving for b:

y = -4x + b

-3 = -4*(1) + b

b = 1

The equation is y = -4x + 1,  This can be rewritten as:

4x + y = 1

Se attached graph.

Answer: C

Step-by-step explanation:

When doing an indirect proof, you begin by assuming the inverse of the statement you want to prove.

Answer:

If you didn't graduate from High school ,Then you are not in college

Step-by-step explanation:

statement :

if you are in college, then you graduated from high school

In the given statement we have :

The Hypothesis is : you are in college

The conclusion is : you graduated from high school

in order to get the contrapositive ,

• first we switch the hypothesis and the conclusion

( H ⇒ C becomes C ⇒ H )

• Second, we negate the hypothesis and the conclusion.

Then

• first ,if you graduated from high school , then you are in college

• second , If you didn't graduate from High school ,Then you are not in college

Answer: 8.6

Step-by-step explanation:

[tex]19.6=2\pi r\left(\frac{130}{360} \right)\\\\r=\frac{19.6}{2\pi \left(\frac{130}{360} \right)}\\\\r \approx 8.6[/tex]

The logarithm of 10 to base 10 is 1

The given parameters are:

Base = 10

Number = 10

So, the expression is:

[tex]\log_{10}10[/tex]

As a general rule;

[tex]\log_{a}a = 1[/tex]

The above means that;

When the base and the number are the same, the logarithm is 1

So, we have:

[tex]\log_{10}10 = 1[/tex]

Hence, the logarithmic value is 1

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Answer:

Horizontal line with y-intercept at (0,0)

Step-by-step explanation:

y - 9 = -9

Adding 9 to both sides:

y = 0

So it is the x axis.

The correct rows in the inequalities are

The rows are given as:

-3x - 4 < x + 4  ⇒ -3x < x

2(x - 5) + 1 ≤ 5  ⇒ 2(x - 5) ≤ 4

-4x ≥ -24  ⇒ x ≤ 6

x = 2y and 2x + 2y > 60  ⇒ 6y > 60

y + 2 ≤ 4 - x and 4 - x ≤ 3y  ⇒ y + 2 ≤ 3y

To determine the correct rows, we simply solve each inequality.

This is done as follows:

-3x - 4 < x + 4

Collect like terms

-3x - x < 4 + 4

Evaluate the like terms

-4x < 8

Divide by -4

x > -2

This means that:

-3x - 4 < x + 4  ⇒ -3x < x is false.

2(x - 5) + 1 ≤ 5  

Subtract 1 from both sides

2(x - 5) ≤ 4

This means that:

2(x - 5) + 1 ≤ 5   ⇒ 2(x - 5) ≤ 4 is true.

-4x ≥ -24  

Divide through by -4

x ≤ 6

This means that:

-4x ≥ -24  ⇒ x ≤ 6 is true.

x = 2y and 2x + 2y > 60

Substitute 2y or x in 2x + 2y > 60

2(2y) + 2y > 60

Evaluate the product

4y + 2y > 60

Evaluate the like terms

6y > 60

This means that:

x = 2y and 2x + 2y > 60  ⇒ 6y > 60 is true.

y + 2 ≤ 4 - x and 4 - x ≤ 3y

We have:

y + 2 ≤ 4 - x and 4 - x ≤ 3y

This can be rewritten as:

y + 2 ≤ 3y

This means that:

y + 2 ≤ 4 - x and 4 - x ≤ 3y  ⇒ y + 2 ≤ 3y is true

Hence, the correct rows are 2, 3, 4 and 5

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Answer:

-8 ≤ x ≤ -1

Step-by-step explanation:

When working with inequalities, closed circles always represent greater than or equal to and less than or equal to signs.  

The x is placed between the -8 and the -1, as it represents all numbers greater than -8 and less than -1

Answer: -8 ≤ x ≤ -1

Step-by-step explanation: :p

Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.

In this problem, the events are:

Event A: Puncture.

Event B: Smashed corner.

The "or" probability is given by:

[tex]P(AUB)=P(A)+P(B)-P(A[/tex]∩[tex]B)[/tex]

5% have a​ puncture, hence [tex]P(A)=0.05[/tex]

8% have a smashed​ corner, hence [tex]P(B)=0.08[/tex]

0.4% have both a puncture and a smashed corner, hence[tex]P(AUB)=0.004[/tex]

Then:

[tex]P(AUB)=0.05+0.08-0.004= 0.126[/tex]

Therefore, The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.

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The numbers of passengers that need to be booked to ensure the cruise line makes a profit, using a compound inequality is x ≥ 2,052 and x ≤ 2,462.

From the information given, we are told that the cruise ship needs to book at least 2,052 passengers to be profitable, but the most passengers the ship can accommodate is 2,462.

Learn x be the number of people that can be accommodated. Therefore, the model is x ≥ 2,052 and x ≤ 2,462.

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Answer:

a = 2

Step-by-step explanation:

Given:

To find:

Steps:

a = V^1/3 = 8^1/3 = 2

Considering the given information in the question, the value of x is [tex]12^{o}[/tex], and that of y is [tex]7.5^{o}[/tex].

A transversal is a line that cuts through two given parallel lines. Thus it intersects each parallel line at a point, forming four angles each.

From the given information in the question, it can be inferred that:

the given bottom right angle of the first intersection and the bottom right angle with the second intersection are congruent (corresponding angle property).

So that,

[tex](5x+4y)^{o}[/tex] = [tex](12y)^{o}[/tex]

[tex]5x^{o}[/tex] = [tex]12y^{o}[/tex] - [tex]4y^{o}[/tex]

[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]............ 1

Also given that the top right angle at the second intersection is a right angle, then;

    [tex]12y^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)

This implies that;

    [tex]12y^{o}[/tex] = [tex]180^{o}[/tex] -    [tex]90^{o}[/tex]

       [tex]12y^{o}[/tex]  =     [tex]90^{o}[/tex]

So that,

y = [tex]\frac{90}{12}[/tex]

y = [tex]7.5^{o}[/tex]

Thus substituting the value of y in equation 1, we have;

[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]........ 1

     = 8(7.5)

5x = 60

x = [tex]\frac{60}{5}[/tex]

x = [tex]12^{o}[/tex]

Therefore, x = [tex]12^{o}[/tex] and y = [tex]7.5^{o}[/tex]

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Kindly contact a 1-on-1 tutor if more explanations are needed.

[tex]x + 4x + 4x + 135 + 135 = 540[/tex]

[tex]9x + 270 = 540[/tex]

[tex]9x = 540 - 270 \\ 9x = 270[/tex]

[tex]x = \frac{270}{9} = 30[/tex]

Answer:

2120 mm

Step-by-step explanation:

→ Convert 2.12 metres into centimetres

2.12 × 100 = 212 cm

→ Multiply by 10 to get into mm

212 × 10 = 2120 mm

Answer:

VY = 28 units

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2 ( length + breadth )

given P = 130 , then

2(5y + 2 + 4y) = 130 ( divide both sides by 2 )

9y + 2 = 65 ( subtract 2 from both sides )

9y = 63 ( divide both sides by 9 )

y = 7

Then

VY = 4y = 4 × 7 = 28

Answer:

3:7

Step-by-step explanation:

So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or 20% is alcohol. So let's just say that x=alcohol and y=water, this means that: [tex]x+y=c[/tex]  where c is the total amount in the glass. This means that: [tex]x=0.20c[/tex]

Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: [tex]j+k=c[/tex] and that: [tex]j=0.40c[/tex].

So if we're going to add the two glasses, we simply add the two sides, and get: [tex]j+x+k+y=2c[/tex]. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: [tex](0.4c+0.2c)+x+k=2c[/tex] Now we can add like terms to get the equation: [tex]0.6c+y+k=2c[/tex]. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.

Answer:

3 : 7

Step-by-step explanation:

We can do this question using a easier way.

For example, A glass contains sugar and water, the ratio to sugar to water is 2 : 5. And the second glass's sugar to water is 2 : 3. The mixture of the first glass is 200 mL. The mixture of the second glass is the same as the first glass.

This kind of glass question, is very important to Math.

Try using this to solve this question.

Answer:

67%

Step-by-step explanation:

268 ÷ 400 = 0.67 = 67%

[tex]\huge\boxed{67\%}[/tex]

This can be solved just with division.

[tex]\dfrac{268\ \text{cars on the wall}}{400\ \text{total cars}}=0.67[/tex]

Multiply the result by [tex]100[/tex] to get a percentage.

[tex]0.67=\boxed{67\%}[/tex]

Answer:

[tex]tan(\alpha)=-\frac{\sqrt{35}}{5}[/tex]

Step-by-step explanation:

Tan can be defined as: [tex]\frac{sin(\theta)}{cos(\theta)}[/tex] as it simplifies to opposite/adjacent. If you know a bit about the unit circle, you'll know that the x-coordinate is going to be cos(theta) and the y-coordinate is going to be sin(theta). Since the sin(theta) is defined as opposite/hypotenuse, and the hypotenuse = 1, so sin(theta) is defined as the opposite side, which is the y-axis. Same thing goes for cos(theta), except the adjacent side is the x-axis.

Using this we can define tan

[tex]sin(\alpha)=-\sqrt{7}\\cos(\alpha)=\sqrt{5}\\\\tan(\alpha)=-\frac{\sqrt{7}}{\sqrt{5}} * \frac{\sqrt{5}}{\sqrt{5}}\\tan(\alpha)=-\frac{\sqrt{7*5}}{5}\\tan(\alpha)=-\frac{\sqrt{35}}{5}\\[/tex]

Answer:

tan α = -√35/5

Step-by-step explanation:

tan α = y/x

tan α = -√7/√5

tan α = -√7/√5 × √5/√5

tan α = -√35/5

Answer: the mass of a neutron is approximately 2,000 times the mass of an electron

Step-by-step explanation:

- the easiest way to solve this (in my opinion) is to simply divide the mass of a neutron by the mass of an electron

- [tex]2 x10^{-24} / (9 x10^{-28} )[/tex]

=  [tex](2/9) x10^{-24--28}[/tex]

=  [tex](2/9)x10^{-24+28}[/tex]

≈  [tex]0.2222x10^{28-24}[/tex]

≈ [tex]0.2222x10^{4}[/tex]

≈ which is approximately 2222    

- so 2222 is approximately 2000 times

- therefore, the mass of a neutron is approximately 2,000 times the mass of an electron

hope this helps :)

Answer:

C. The mass of a neutron is approximately 2,000 times the mass of an electron.

Step-by-step explanation:

Divide the mass of the neutron by the mass of the electron:

[tex]\implies \sf \dfrac{mass\:of\:neutron}{mass \: of \: electron}=\dfrac{2 \times 10^{-24}}{9 \times 10^{-28}}[/tex]

Rewrite:

[tex]\implies \sf \dfrac{2}{9} \times \dfrac{10^{-24}}{10^{-28}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \sf \dfrac{2}{9} \times 10^{-24-(-28)}[/tex]

Simplify:

[tex]\implies \sf \dfrac{2}{9} \times 10^{4}[/tex]

[tex]\implies \sf 0.\.{2} \times 10^{4} \approx 2000[/tex]

Therefore, the mass of a neutron is approximately 2,000 times the mass of an electron.

Check

[tex]\begin{aligned}\textsf{mass of neutron} & = \sf \textsf{mass of electron} \times 2000\\\implies \textsf{mass of neutron} & =\sf 9 \times 10^{-28}\times 2000\\& =\sf 9 \times 10^{-28}\times 2 \times 10^3\\& =\sf 18 \times 10^{-28+3}\\& =\sf 18 \times 10^{-25}\\& = \sf 1.8 \times 10^{-24}\\& \approx \sf 2 \times 10^{-24}\end{aligned}[/tex]

The number of blue marbles in the bag is 18.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of choosing a green marble = total number of green marbles / total number of marbles

0.55 = 22/x

x = 22 / 0.55

x = 40

Total number of blue marbles = 40 - 22 = 18

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Answer:

12

Step-by-step explanation:

16/4=4

4+8=12

The probability of drawing two 10's is P = 1/221, so the correct option is D.

We know that in the deck of 52 cards, we have 4 10's.

Then, the probability of drawing the first 10 is:

p = 4/52.

At this point, we have 3 10's in the deck, and a total of 51 cards (because we already took one 10).

The probability of getting another is:

q = 3/51

The joint probability (of getting both 10's, one after the other) is given by the product of the individual probabilities:

P = p*q = (4/52)*(3/51) = (1/13)*(1/17) = 1/221

Then the correct option is D.

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